Using a fermionic version of the Lax pair formulation, we construct an integrable small-polaron model with general open boundary conditions. The Lax pair and the boundary supermatrices K± for the model are obtained. This provides a direct proof of the integrability of the model.
Abstract Based on the Lax pair formulation, we study the integrable conditions of the Osp(1∣2) spin chain with open boundaries. We consider both the non-graded and graded versions of the Osp(1∣2) chain. The Lax pair operators M ± for the boundaries can be induced by the Lax operator M j for the bulk of the system. They correspond to the reflection equations (RE) and the Yang–Baxter equation, respectively. We further calculate the boundary K-matrices for both the non-graded and graded versions of the model with open boundaries. The double row monodromy matrix and transfer matrix of the spin chain have also been constructed. The K-matrices obtained from the Lax pair formulation are consistent with those from Sklyanin’s RE. This construction is another way to prove the quantum integrability of the Osp(1∣2) chain. We find that the Lax pair formulation has advantages in dealing with the boundary terms of the supersymmetric model.